"We have looked at this thing from every which way," Thomas told the insider newsletter. "It doesn't make sense to get in. We don't see a chance to win. I don't want to be a second candidate against an incumbent."
His decision means Mourdock will likely have a clear shot against Lugar in the May primary. The state filing deadline is Feb. 21.
Thomas also said he would not endorse Lugar or Mourdock.
In 2010, Thomas spent $600,000 out of his own pocket to challenge then-Rep. Mark Souder (R-Ind.). Thomas lost his primary bid to Souder by about 14 points in what was a crowded GOP field.
Vice President Joe Biden waits to conduct a mock swearing-in ceremony with Sen. Brian Schatz, D-Hawaii, in the Capitol's Old Senate Chamber, December 2, 2014. Schatz was sworn in to serve the remainder of his term since he was appointed to the seat after Sen. Daniel Inouye, D-Hawaii, passed away.